Airfoil shape and platform contour for turbine rotor blades

ABSTRACT

A turbine rotor blade including an airfoil that extends from a platform. The platform may include a first portion of a nominal platform contour substantially in accordance with Cartesian coordinate values of X′, Y′, and Z′ as set forth in Table II. The Cartesian coordinate values of X′, Y′, and Z′ are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X′, Y′, and Z′ by a height of the airfoil defined along a Z′ axis. The X′ and Y′ values of the first portion are coordinate values that, when connected by smooth continuing arcs, define contour lines of the first portion of the nominal airfoil profile at each Z′ coordinate value. The contour lines may be joined smoothly with one another to form the first portion.

BACKGROUND OF THE INVENTION

The subject matter disclosed herein relates to turbine engine airfoils and, more specifically, to airfoils of turbine rotor blades.

Some aircraft and/or power plant systems, for example certain jet aircraft, gas turbines, and combined cycle power plant systems, employ turbines (also referred to as turbomachines) in their design and operation. These turbines employ airfoils (e.g., turbine rotor blades, blades, airfoils, etc.) which during operation are exposed to fluid flows. These airfoils—and the endwalls or platforms from which the airfoils extend—are configured to aerodynamically interact with the fluid flows and generate energy (e.g., creating thrust, turning kinetic energy to mechanical energy, thermal energy to mechanical energy, etc.) from these fluid flows as part of power generation. As a result of this interaction and conversion, the aerodynamic characteristics and losses of the airfoils and platforms have an impact on system and turbine operation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION OF THE INVENTION

Aspects and advantages are set forth below in the following description, or may be obvious from the description, or may be learned through practice.

According to an exemplary embodiment, a turbine rotor blade includes an airfoil that extends from a platform, with the platform including a first portion of a nominal platform contour substantially in accordance with Cartesian coordinate values of X′, Y′, and Z′ as set forth in Table II. The Cartesian coordinate values of X′, Y′, and Z′ are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X′, Y′, and Z′ by a height of the airfoil defined along a Z′ axis. The X′ and Y′ values of the first portion are coordinate values that, when connected by smooth continuing arcs, define contour lines of the first portion of the nominal airfoil profile at each Z′ coordinate value. The contour lines may be joined smoothly with one another to form the first portion.

According to an exemplary embodiment, the present disclosure includes a turbine rotor blade having an airfoil that includes a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a height of the airfoil defined along the Z axis. The X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value. The pressure side sections may be joined smoothly with one another to form the pressure side portion.

According to another exemplary embodiment, the present disclosure includes a turbine rotor blade having an airfoil that includes a suction side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a suction side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a height of the airfoil defined along the Z axis. The X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value. The suction side sections may be joined smoothly with one another to form the suction side portion.

According to another exemplary embodiment, the present disclosure includes a turbine engine that has an airfoil that includes: a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I; and a suction side portion of the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a height of the airfoil defined along the Z axis. The X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value. The pressure side sections may be joined smoothly with one another to form the pressure side portion. The X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value. The suction side sections may be joined smoothly with one another to form the suction side portion.

Those of ordinary skill in the art will better appreciate the features and aspects of such embodiments, and others, upon review of the specification.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of various embodiments, including the best mode thereof to one skilled in the art, is set forth more particularly in the remainder of the specification, including reference to the accompanying figures, in which:

FIG. 1 is a schematic representation of an exemplary turbine having multiple stages with each stage including alternating rows of turbine rotor blades and stationary vanes or nozzles according to at least one embodiment of the present disclosure;

FIG. 2 is a perspective view of a turbine rotor blade according to at least one embodiment of the present disclosure; and

FIG. 3 is a top view showing surface contour of a platform at the base of a turbine rotor blade according to at least one embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE INVENTION

One or more specific embodiments of the present subject matter will be described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

When introducing elements of various embodiments of the present subject matter, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements.

Referring now to the drawings, particularly to FIG. 1, there is illustrated an exemplary turbine 10 of a combustion or gas turbine 12 including a plurality of turbine stages arranged in serial flow order. Each stage of the turbine includes a row of turbine vanes or nozzles disposed axially adjacent to a corresponding row of turbine rotor blades. While four stages are illustrated in FIG. 1, the exact number of stages of the turbine 10 is a choice of engineering design, and may be more or less than the four stages shown. The four stages are merely exemplary of one turbine design, and are not intended to limit the presently claimed turbine rotor blade in any manner.

As depicted in FIG. 1, the first stage includes a plurality of turbine nozzles 100 and a plurality of turbine rotor blades 150. The turbine nozzles 100 are annularly arranged about an axis of a turbine rotor 14, while the turbine rotor blades 150 are annularly arranged about and coupled to the turbine rotor 14. A second stage of the turbine 12 includes a plurality of turbine nozzles 200 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 250 annularly arranged about and coupled to the turbine rotor 14. A third stage of the turbine 12 includes a plurality of turbine nozzles 300 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 350 annularly arranged about and coupled to the turbine rotor 14. In particular embodiments, the turbine 12 may further include a fourth stage, which also includes plurality of turbine nozzles 400 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 450 annularly arranged about and coupled to the turbine rotor 14. As will be appreciated, the turbine nozzles 100, 200, 300, 400 may be coupled to the casing 16 of the turbine 12 and remain stationary during operation.

It will be appreciated that the turbine nozzles 100, 200, 300 and 400 and turbine rotor blades 150, 250, 350 and 450 are disposed or at least partially disposed within a working fluid or hot gas path 18 of the turbine 12. The various stages of the turbine 10 at least partially define the hot gas path 18 through which combustion gases, as indicated by arrows 20, flow during operation of the gas turbine 12.

FIG. 2 provides a perspective view of an exemplary turbine rotor blade 50, as may be incorporated in one of the stages of the turbine 12. In a preferred embodiment of the present disclosure, the turbine rotor blade 50 (as described by the points included within Table I below) is a turbine rotor blade 250 of the plurality of the turbine rotor blades 250 used in the second stage of the turbine 12, as shown in FIG. 1. As illustrated in FIG. 2, the turbine rotor blade 50 includes an airfoil 52 having a pressure side 54 and an opposing suction side 56. The pressure side 54 and the suction side 56 meet or intersect at a leading edge 58 and a trailing edge 60 of the airfoil 52. A chord line 62 extends between the leading edge 58 and the trailing edge 60 such that pressure and suction sides 54, 56 can be said to extend in chord or chordwise between the leading edge 58 and the trailing edge 60.

The airfoil 52 further includes a first end or root 64 which intersects with and extends radially outwardly from an endwall or platform 66 of the turbine rotor blade 50. The airfoil 52 terminates radially at a second end or radial tip 68 of the airfoil 52. The pressure and suction sides 54, 56 can be said to extend in span or in a span-wise direction 70 (along the height of the airfoil 52) between the platform 66 and the radial tip 68 of the airfoil 52. In other words, each turbine rotor blade 50 includes an airfoil 52 having opposing pressure and suction sides 54, 56 that extend in chord or chordwise 62 between opposing leading and trailing edges 58, 60 and that extend in span or span-wise 70 between the platform 66 and the radial tip 68 of the airfoil 52.

In particular configurations, the airfoil 52 may include a fillet 72 formed between the platform 66 and the airfoil 52 proximate to the root 64. The fillet 72 can include a weld or braze fillet, which can be formed via conventional MIG welding, TIG welding, brazing, etc., and can include a profile that reduces fluid dynamic losses. In particular embodiments, the platform 66, airfoil 52 and the fillet 72 can be formed as a single component, such as by casting and/or machining and/or 3D printing and/or any other suitable technique now known or later developed and/or discovered. In particular configurations, the turbine rotor blade 50 includes a mounting portion 74 which is formed to connect and/or to secure the turbine rotor blade 50 to the rotor shaft 14.

The airfoil 52 of the turbine rotor blade 50 has a profile at any cross-section taken between the platform 66 or the root 64 and the radial tip 68. In accordance with the present disclosure, the X, Y, and Z values of the profile are given in Table I as percentage values of the airfoil span or height. As one example only, the height of the airfoil 52 of the rotor blade 50 may be from about 2 inches to about 50 inches. As another example, the height of the airfoil 52 of the rotor blade 50 may be from about 3 inches to about 10 inches. However, it is to be understood that heights below or above this range may also be employed as desired in the specific application.

A hot gas path of a gas turbine requires airfoils that meet system requirements of aerodynamic and mechanical blade loading and efficiency. Additionally, the platforms and fillets at the base of the airfoils impact aerodynamic characteristics and losses of the rotor blade and must also satisfy system requirements of aerodynamic and mechanical blade loading and efficiency. That is, the aerodynamic characteristics and losses associated with each of the airfoil, the fillet, and/or the platform, separately, as well as the manner in which these components function together, significantly impact performance, thrust, efficiency, and power. As will be seen, to define the shape of these components, there is a unique set or locus of points in space that meet the stage requirements and that can be manufactured. This unique locus of points meets the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine to run in an efficient, safe and smooth manner. These points are unique and specific to the system.

In accordance with the embodiments of the present disclosure, the locus of points that defines an airfoil profile of a turbine rotor blade includes a set of points with X, Y, and Z dimensions relative to a reference origin coordinate system, as provided in Table I and shown in FIG. 2, respectively. As provided below, in accordance with an alternative embodiment of the present disclosure, the locus of points that defines a contour of a platform of a turbine rotor blade includes a set of points with X′, Y′, and Z′ dimensions relative to a reference origin coordinate system, as provided in Table II and shown in FIG. 3, respectively.

The Cartesian coordinate system of X, Y, and Z values given in Table I below defines the airfoil profile of the turbine rotor blade 50 at various locations along its length or span or, as used herein, height. As shown in FIG. 2, the point data origin 76 is defined at or proximate to the root 64 at the leading edge 58 of the airfoil 52. In one embodiment, as presented in Table I below, the point data origin 76 is defined at or proximate to (above or below) a transition or intersection line 78 defined between the fillet 72 and the airfoil 52. The point data origin 76 corresponds to the non-dimensional Z value of Table I (presented below) at Z equals 0.

The coordinate values for the X, Y, and Z coordinates are set forth in non-dimensionalized units in Table I, although units of dimensions may be used when the values are appropriately converted. That is, the X, Y, and Z values set forth in Table I are expressed in non-dimensional form (X, Y, and Z) from 0% to 100% of the radial span 70 or height of the airfoil. As one example, the Cartesian coordinate values of X, Y, and Z may be convertible to dimensional distances by multiplying the X, Y, and Z values by a height of the airfoil at the leading edge 58 and/or multiplying by a constant number. As another example, the Cartesian coordinate values of X, Y, and Z may be convertible to dimensional distances by multiplying the X, Y, and Z values by a height of the airfoil at the trailing edge 60 and/or multiplying by a constant number. Thus, to convert the Z value to a Z coordinate value, for example, in inches, the non-dimensional Z value given in Table I is multiplied by the height of the airfoil in inches.

As described above, the Cartesian coordinate system has orthogonally-related X, Y, and Z axes, where the X axis lies generally parallel to a centerline of the rotor shaft 14, i.e., the rotary axis and a positive X coordinate value is axial toward an aft, i.e., exhaust end, of the turbine 10. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor, and the positive Z coordinate value extends radially outwardly toward the radial tip 68 of the airfoil 52. All the values in Table I are given at room temperature and do not include the fillet 72.

By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the airfoil shape or profile sections (which may be referred to as “pressure side sections” on the pressure side and “suction side sections” on the suction side) of the airfoil 52 of the turbine rotor blade 50 along the span or height of the airfoil 52 can be ascertained. Thus, by connecting the X and Y values with smooth continuing arcs, each profile section (which may include a pressure side section and suction side section) at each distance Z is determined. The airfoil profiles of the various surface locations between the distances Z can then be determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The Table I values are generated and shown to four decimal places for determining the profile of the airfoil. As the turbine rotor blade heats up during operation of the gas turbine, mechanical stresses and elevated temperatures will cause a change in the X, Y, and Z values. Accordingly, it should be understood that the values for the nominal airfoil profile given in Table I represent ambient, non-operating or non-hot conditions (e.g., room temperature) and are for an uncoated airfoil.

There are typical manufacturing tolerances as well as coatings which may be accounted for in the actual profile of the airfoil 52. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, may be additive to the X and Y values given in Table I below. Accordingly, a distance of +/−5% in a direction normal to any airfoil surface location or about +/−5% of the chord 62 in a direction nominal to any airfoil surface location may define an airfoil profile envelope for this particular airfoil design, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in Table I below at the same temperature. According to another example, a tolerance of about 10-20% of a thickness of the airfoil's trailing edge 60 in a direction normal to any airfoil surface location may define a range of variation between measured points on an actual airfoil surface and ideal positions as embodied by the invention in Table I. As should further be understood, the data provided in Table I is scalable and the geometry pertains to all aerodynamic scales and/or RPM ranges. The design of the airfoil 52 for the turbine rotor blade 50 is robust to this range of variation without impairment of mechanical and aerodynamic functions.

TABLE I SUCTION SIDE PRESSURE SIDE X (%) Y (%) Z (%) X (%) Y (%) Z (%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 −0.2028 0.5110 0.0000 0.2343 −0.3110 0.0000 −0.2630 1.0617 0.0000 0.5384 −0.5589 0.0000 −0.2082 1.6138 0.0000 0.8891 −0.7261 0.0000 −0.0699 2.1454 0.0000 1.2590 −0.8480 0.0000 0.1260 2.6591 0.0000 1.6357 −0.9549 0.0000 0.3576 3.1550 0.0000 2.0166 −1.0480 0.0000 0.6151 3.6372 0.0000 2.4002 −1.1247 0.0000 0.8960 4.1058 0.0000 2.7851 −1.1932 0.0000 1.1973 4.5647 0.0000 3.1701 −1.2576 0.0000 1.5138 5.0113 0.0000 3.5564 −1.3234 0.0000 1.8426 5.4469 0.0000 3.9427 −1.3891 0.0000 2.1823 5.8703 0.0000 4.3291 −1.4535 0.0000 2.5317 6.2854 0.0000 4.7168 −1.5111 0.0000 2.8879 6.6922 0.0000 5.1031 −1.5590 0.0000 3.2523 7.0936 0.0000 5.4908 −1.6015 0.0000 3.6208 7.4909 0.0000 5.8812 −1.6439 0.0000 3.9934 7.8827 0.0000 6.2730 −1.6905 0.0000 4.3743 8.2677 0.0000 6.6662 −1.7426 0.0000 4.7606 8.6472 0.0000 7.0580 −1.7933 0.0000 5.1551 9.0198 0.0000 7.4471 −1.8179 0.0000 5.5552 9.3869 0.0000 7.8307 −1.7837 0.0000 5.9607 9.7486 0.0000 8.2088 −1.6850 0.0000 6.3758 10.1021 0.0000 8.5814 −1.5508 0.0000 6.7964 10.4487 0.0000 8.9554 −1.4138 0.0000 7.2183 10.7980 0.0000 9.3294 −1.2891 0.0000 7.6663 11.0980 0.0000 9.7061 −1.1754 0.0000 8.1595 11.3131 0.0000 10.0829 −1.0672 0.0000 8.6732 11.4912 0.0000 10.4610 −0.9644 0.0000 9.1979 11.6309 0.0000 10.8418 −0.8672 0.0000 9.7322 11.7296 0.0000 11.2227 −0.7822 0.0000 10.2733 11.7857 0.0000 11.6076 −0.7083 0.0000 10.8158 11.8035 0.0000 11.9940 −0.6480 0.0000 11.3583 11.7844 0.0000 12.3830 −0.6028 0.0000 11.8981 11.7268 0.0000 12.7748 −0.5713 0.0000 12.4324 11.6364 0.0000 13.1708 −0.5535 0.0000 12.9612 11.5131 0.0000 13.5653 −0.5521 0.0000 13.4790 11.3583 0.0000 13.9599 −0.5685 0.0000 13.9873 11.1747 0.0000 14.3517 −0.6000 0.0000 14.4859 10.9651 0.0000 14.7407 −0.6466 0.0000 14.9750 10.7309 0.0000 15.1257 −0.7069 0.0000 15.4531 10.4761 0.0000 15.5079 −0.7795 0.0000 15.9203 10.2034 0.0000 15.8888 −0.8644 0.0000 16.3765 9.9116 0.0000 16.2682 −0.9617 0.0000 16.8231 9.6061 0.0000 16.6450 −1.0699 0.0000 17.2587 9.2856 0.0000 17.0203 −1.1905 0.0000 17.6848 8.9527 0.0000 17.3930 −1.3206 0.0000 18.0999 8.6088 0.0000 17.7601 −1.4604 0.0000 18.5040 8.2554 0.0000 18.1259 −1.6070 0.0000 18.8999 7.8910 0.0000 18.4862 −1.7604 0.0000 19.2876 7.5197 0.0000 18.8424 −1.9207 0.0000 19.6657 7.1388 0.0000 19.1958 −2.0878 0.0000 20.0384 6.7511 0.0000 19.5465 −2.2591 0.0000 20.4014 6.3552 0.0000 19.8931 −2.4358 0.0000 20.7590 5.9525 0.0000 20.2370 −2.6166 0.0000 21.1097 5.5442 0.0000 20.5781 −2.8029 0.0000 21.4549 5.1291 0.0000 20.9165 −2.9947 0.0000 21.7919 4.7085 0.0000 21.2521 −3.1906 0.0000 22.1248 4.2839 0.0000 21.5850 −3.3920 0.0000 22.4522 3.8537 0.0000 21.9138 −3.6002 0.0000 22.7742 3.4194 0.0000 22.2399 −3.8126 0.0000 23.0906 2.9824 0.0000 22.5632 −4.0318 0.0000 23.4030 2.5413 0.0000 22.8810 −4.2565 0.0000 23.7112 2.0974 0.0000 23.1975 −4.4880 0.0000 24.0153 1.6508 0.0000 23.5085 −4.7264 0.0000 24.3167 1.2028 0.0000 23.8167 −4.9688 0.0000 24.6154 0.7521 0.0000 24.1208 −5.2182 0.0000 24.9099 0.3000 0.0000 24.4222 −5.4730 0.0000 25.2045 −0.1534 0.0000 24.7195 −5.7305 0.0000 25.4963 −0.6083 0.0000 25.0140 −5.9922 0.0000 25.7867 −1.0631 0.0000 25.3058 −6.2580 0.0000 26.0771 −1.5179 0.0000 25.5963 −6.5251 0.0000 26.3676 −1.9741 0.0000 25.8826 −6.7950 0.0000 26.6580 −2.4303 0.0000 26.1675 −7.0662 0.0000 26.9484 −2.8851 0.0000 26.4498 −7.3402 0.0000 27.2389 −3.3413 0.0000 26.7292 −7.6156 0.0000 27.5293 −3.7975 0.0000 27.0073 −7.8951 0.0000 27.8183 −4.2537 0.0000 27.2827 −8.1759 0.0000 28.1074 −4.7099 0.0000 27.5553 −8.4595 0.0000 28.3965 −5.1661 0.0000 27.8252 −8.7458 0.0000 28.6842 −5.6237 0.0000 28.0923 −9.0362 0.0000 28.9718 −6.0812 0.0000 28.3554 −9.3280 0.0000 29.2582 −6.5402 0.0000 28.6157 −9.6239 0.0000 29.5445 −7.0005 0.0000 28.8732 −9.9226 0.0000 29.8281 −7.4622 0.0000 29.1267 −10.2254 0.0000 30.1117 −7.9238 0.0000 29.3774 −10.5309 0.0000 30.3939 −8.3869 0.0000 29.6239 −10.8405 0.0000 30.6747 −8.8513 0.0000 29.8664 −11.1514 0.0000 30.9542 −9.3157 0.0000 30.1062 −11.4652 0.0000 31.2336 −9.7801 0.0000 30.3432 −11.7789 0.0000 31.5117 −10.2459 0.0000 30.5774 −12.0940 0.0000 31.7871 −10.7131 0.0000 30.8090 −12.4118 0.0000 32.0584 −11.1830 0.0000 31.0364 −12.7324 0.0000 32.3337 −11.6501 0.0000 31.2597 −13.0584 0.0000 32.6187 −12.1159 0.0000 31.5008 −13.3721 0.0000 32.7324 −12.3639 0.0000 31.6570 −13.4845 0.0000 32.8461 −12.6118 0.0000 31.8131 −13.5968 0.0000 32.8790 −12.9543 0.0000 32.0543 −13.6544 0.0000 32.7735 −13.2804 0.0000 32.3050 −13.6324 0.0000 32.5351 −13.5297 0.0000 32.5351 −13.5297 0.0000 0.3000 0.4658 2.6714 0.3000 0.4658 2.6714 0.0644 0.9192 2.6714 0.6165 0.2192 2.6714 0.0192 1.4316 2.6714 0.9960 0.0877 2.6714 0.0959 1.9412 2.6714 1.3974 0.0548 2.6714 0.2507 2.4330 2.6714 1.8001 0.0781 2.6714 0.4535 2.9070 2.6714 2.1988 0.1356 2.6714 0.6932 3.3646 2.6714 2.5947 0.2151 2.6714 0.9590 3.8057 2.6714 2.9851 0.3137 2.6714 1.2480 4.2345 2.6714 3.3728 0.4261 2.6714 1.5563 4.6469 2.6714 3.7578 0.5466 2.6714 1.8823 5.0483 2.6714 4.1400 0.6740 2.6714 2.2234 5.4360 2.6714 4.5222 0.8028 2.6714 2.5769 5.8114 2.6714 4.9044 0.9316 2.6714 2.9386 6.1785 2.6714 5.2867 1.0590 2.6714 3.3112 6.5361 2.6714 5.6689 1.1878 2.6714 3.6920 6.8854 2.6714 6.0511 1.3165 2.6714 4.0811 7.2238 2.6714 6.4333 1.4467 2.6714 4.4770 7.5553 2.6714 6.8155 1.5755 2.6714 4.8812 7.8759 2.6714 7.1978 1.7042 2.6714 5.2935 8.1869 2.6714 7.5813 1.8289 2.6714 5.7127 8.4883 2.6714 7.9649 1.9508 2.6714 6.1401 8.7759 2.6714 8.3526 2.0659 2.6714 6.5785 9.0499 2.6714 8.7403 2.1728 2.6714 7.0251 9.3075 2.6714 9.1321 2.2686 2.6714 7.4841 9.5431 2.6714 9.5267 2.3536 2.6714 7.9540 9.7582 2.6714 9.9240 2.4262 2.6714 8.4335 9.9473 2.6714 10.3226 2.4824 2.6714 8.9239 10.1075 2.6714 10.7240 2.5221 2.6714 9.4226 10.2404 2.6714 11.1268 2.5454 2.6714 9.9281 10.3418 2.6714 11.5296 2.5509 2.6714 10.4404 10.4117 2.6714 11.9323 2.5385 2.6714 10.9542 10.4487 2.6714 12.3351 2.5084 2.6714 11.4706 10.4528 2.6714 12.7351 2.4618 2.6714 11.9858 10.4240 2.6714 13.1338 2.3988 2.6714 12.4981 10.3637 2.6714 13.5297 2.3193 2.6714 13.0064 10.2719 2.6714 13.9215 2.2262 2.6714 13.5078 10.1500 2.6714 14.3092 2.1180 2.6714 14.0010 9.9993 2.6714 14.6942 1.9974 2.6714 14.4873 9.8240 2.6714 15.0750 1.8631 2.6714 14.9627 9.6253 2.6714 15.4517 1.7193 2.6714 15.4298 9.4048 2.6714 15.8230 1.5631 2.6714 15.8860 9.1636 2.6714 16.1915 1.3987 2.6714 16.3326 8.9061 2.6714 16.5559 1.2247 2.6714 16.7696 8.6307 2.6714 16.9149 1.0425 2.6714 17.1971 8.3417 2.6714 17.2710 0.8521 2.6714 17.6149 8.0389 2.6714 17.6218 0.6535 2.6714 18.0232 7.7238 2.6714 17.9697 0.4493 2.6714 18.4232 7.3964 2.6714 18.3136 0.2384 2.6714 18.8150 7.0608 2.6714 18.6533 0.0219 2.6714 19.1972 6.7142 2.6714 18.9890 −0.2014 2.6714 19.5712 6.3593 2.6714 19.3219 −0.4288 2.6714 19.9384 5.9963 2.6714 19.6507 −0.6617 2.6714 20.2987 5.6264 2.6714 19.9767 −0.9001 2.6714 20.6521 5.2497 2.6714 20.2987 −1.1425 2.6714 20.9973 4.8675 2.6714 20.6179 −1.3905 2.6714 21.3384 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80.0000 16.5326 8.9198 80.0000 14.9517 4.9579 80.0000 16.7655 8.5691 80.0000 15.1613 4.6647 80.0000 16.9957 8.2156 80.0000 15.3695 4.3715 80.0000 17.2204 7.8594 80.0000 15.5764 4.0784 80.0000 17.4437 7.5005 80.0000 15.7819 3.7825 80.0000 17.6629 7.1402 80.0000 15.9860 3.4865 80.0000 17.8793 6.7785 80.0000 16.1902 3.1893 80.0000 18.0944 6.4155 80.0000 16.3915 2.8920 80.0000 18.3054 6.0511 80.0000 16.5929 2.5947 80.0000 18.5150 5.6853 80.0000 16.7943 2.2960 80.0000 18.7232 5.3182 80.0000 16.9929 1.9960 80.0000 18.9287 4.9510 80.0000 17.1930 1.6974 80.0000 19.1328 4.5811 80.0000 17.3916 1.3974 80.0000 19.3356 4.2112 80.0000 17.5889 1.0960 80.0000 19.5356 3.8400 80.0000 17.7861 0.7946 80.0000 19.7342 3.4687 80.0000 17.9821 0.4932 80.0000 19.9301 3.0961 80.0000 18.1780 0.1918 80.0000 20.1260 2.7221 80.0000 18.3725 −0.1110 80.0000 20.3206 2.3481 80.0000 18.5670 −0.4151 80.0000 20.5124 1.9727 80.0000 18.7602 −0.7179 80.0000 20.7042 1.5974 80.0000 18.9534 −1.0220 80.0000 20.8932 1.2206 80.0000 19.1451 −1.3261 80.0000 21.0823 0.8425 80.0000 19.3356 −1.6316 80.0000 21.2686 0.4658 80.0000 19.5260 −1.9371 80.0000 21.4549 0.0863 80.0000 19.7164 −2.2426 80.0000 21.6398 −0.2918 80.0000 19.9055 −2.5481 80.0000 21.8220 −0.6726 80.0000 20.0945 −2.8550 80.0000 22.0042 −1.0521 80.0000 20.2836 −3.1619 80.0000 22.1837 −1.4343 80.0000 20.4726 −3.4687 80.0000 22.3632 −1.8152 80.0000 20.6603 −3.7756 80.0000 22.5413 −2.1974 80.0000 20.8480 −4.0825 80.0000 22.7180 −2.5810 80.0000 21.0343 −4.3907 80.0000 22.8947 −2.9632 80.0000 21.2220 −4.6976 80.0000 23.0687 −3.3468 80.0000 21.4083 −5.0058 80.0000 23.2427 −3.7318 80.0000 21.5933 −5.3141 80.0000 23.4167 −4.1154 80.0000 21.7796 −5.6237 80.0000 23.5879 −4.5003 80.0000 21.9645 −5.9319 80.0000 23.7578 −4.8866 80.0000 22.1481 −6.2415 80.0000 23.9277 −5.2730 80.0000 22.3317 −6.5511 80.0000 24.0948 −5.6593 80.0000 22.5139 −6.8607 80.0000 24.2619 −6.0470 80.0000 22.6961 −7.1717 80.0000 24.4291 −6.4347 80.0000 22.8769 −7.4827 80.0000 24.5948 −6.8224 80.0000 23.0564 −7.7951 80.0000 24.7606 −7.2101 80.0000 23.2358 −8.1060 80.0000 24.9250 −7.5978 80.0000 23.4139 −8.4198 80.0000 25.0894 −7.9855 80.0000 23.5907 −8.7335 80.0000 25.2524 −8.3745 80.0000 23.7674 −9.0472 80.0000 25.4154 −8.7636 80.0000 23.9414 −9.3623 80.0000 25.5771 −9.1527 80.0000 24.1154 −9.6774 80.0000 25.7360 −9.5431 80.0000 24.2893 −9.9925 80.0000 25.8949 −9.9336 80.0000 24.4606 −10.3103 80.0000 26.0525 −10.3254 80.0000 24.6318 −10.6268 80.0000 26.2114 −10.7158 80.0000 24.8003 −10.9446 80.0000 26.3703 −11.1062 80.0000 24.9675 −11.2638 80.0000 26.5306 −11.4967 80.0000 25.1319 −11.5830 80.0000 26.6840 −11.8899 80.0000 25.2963 −11.9022 80.0000 26.7477 −12.0919 80.0000 25.4579 −12.2241 80.0000 26.8114 −12.2940 80.0000 25.6223 −12.5474 80.0000 26.8142 −12.5611 80.0000 25.8141 −12.8475 80.0000 26.6936 −12.8036 80.0000 26.1306 −13.0091 80.0000 26.4785 −12.9666 80.0000 26.4785 −12.9666 80.0000 4.6661 12.9735 90.0007 4.6661 12.9735 90.0007 4.6277 13.2434 90.0007 4.7592 12.7611 90.0007 4.6674 13.5146 90.0007 4.9003 12.5762 90.0007 4.7168 13.6420 90.0007 4.9873 12.4988 90.0007 4.7661 13.7694 90.0007 5.0743 12.4214 90.0007 4.9921 14.1256 90.0007 5.3880 12.2433 90.0007 5.2730 14.4435 90.0007 5.7278 12.1323 90.0007 5.5935 14.7161 90.0007 6.0799 12.0693 90.0007 5.9401 14.9503 90.0007 6.4361 12.0364 90.0007 6.3018 15.1599 90.0007 6.7936 12.0186 90.0007 6.6785 15.3463 90.0007 7.1512 12.0036 90.0007 7.0717 15.4997 90.0007 7.5101 11.9816 90.0007 7.4745 15.6107 90.0007 7.8663 11.9474 90.0007 7.8841 15.6805 90.0007 8.2170 11.8953 90.0007 8.2978 15.7093 90.0007 8.5636 11.8227 90.0007 8.7157 15.7024 90.0007 8.9075 11.7282 90.0007 9.1308 15.6572 90.0007 9.2472 11.6104 90.0007 9.5390 15.5778 90.0007 9.5828 11.4679 90.0007 9.9404 15.4654 90.0007 9.9075 11.3049 90.0007 10.3336 15.3230 90.0007 10.2199 11.1213 90.0007 10.7144 15.1545 90.0007 10.5213 10.9213 90.0007 11.0816 14.9640 90.0007 10.8117 10.7062 90.0007 11.4364 14.7558 90.0007 11.0912 10.4774 90.0007 11.7789 14.5325 90.0007 11.3624 10.2391 90.0007 12.1118 14.2928 90.0007 11.6255 9.9897 90.0007 12.4351 14.0393 90.0007 11.8803 9.7322 90.0007 12.7502 13.7722 90.0007 12.1269 9.4678 90.0007 13.0557 13.4927 90.0007 12.3680 9.1965 90.0007 13.3516 13.2023 90.0007 12.6022 8.9212 90.0007 13.6393 12.9050 90.0007 12.8324 8.6417 90.0007 13.9160 12.5995 90.0007 13.0557 8.3595 90.0007 14.1845 12.2871 90.0007 13.2749 8.0732 90.0007 14.4448 11.9707 90.0007 13.4900 7.7855 90.0007 14.6983 11.6474 90.0007 13.7009 7.4950 90.0007 14.9449 11.3213 90.0007 13.9078 7.2019 90.0007 15.1860 10.9898 90.0007 14.1119 6.9060 90.0007 15.4216 10.6542 90.0007 14.3133 6.6087 90.0007 15.6518 10.3158 90.0007 14.5120 6.3087 90.0007 15.8764 9.9733 90.0007 14.7079 6.0086 90.0007 16.0970 9.6281 90.0007 14.9024 5.7059 90.0007 16.3134 9.2787 90.0007 15.0956 5.4017 90.0007 16.5272 8.9266 90.0007 15.2860 5.0976 90.0007 16.7368 8.5732 90.0007 15.4750 4.7907 90.0007 16.9436 8.2170 90.0007 15.6641 4.4839 90.0007 17.1477 7.8594 90.0007 15.8504 4.1770 90.0007 17.3491 7.5005 90.0007 16.0367 3.8688 90.0007 17.5478 7.1402 90.0007 16.2217 3.5591 90.0007 17.7451 6.7799 90.0007 16.4066 3.2495 90.0007 17.9410 6.4169 90.0007 16.5888 2.9399 90.0007 18.1355 6.0538 90.0007 16.7724 2.6289 90.0007 18.3273 5.6894 90.0007 16.9532 2.3180 90.0007 18.5177 5.3250 90.0007 17.1341 2.0070 90.0007 18.7068 4.9592 90.0007 17.3149 1.6946 90.0007 18.8944 4.5935 90.0007 17.4943 1.3823 90.0007 19.0808 4.2263 90.0007 17.6724 1.0699 90.0007 19.2643 3.8592 90.0007 17.8505 0.7562 90.0007 19.4479 3.4907 90.0007 18.0286 0.4425 90.0007 19.6301 3.1221 90.0007 18.2054 0.1288 90.0007 19.8096 2.7536 90.0007 18.3821 −0.1849 90.0007 19.9890 2.3837 90.0007 18.5588 −0.4987 90.0007 20.1658 2.0125 90.0007 18.7342 −0.8138 90.0007 20.3425 1.6412 90.0007 18.9095 −1.1275 90.0007 20.5178 1.2699 90.0007 19.0849 −1.4426 90.0007 20.6918 0.8973 90.0007 19.2602 −1.7577 90.0007 20.8658 0.5247 90.0007 19.4356 −2.0727 90.0007 21.0384 0.1507 90.0007 19.6096 −2.3878 90.0007 21.2097 −0.2233 90.0007 19.7849 −2.7029 90.0007 21.3795 −0.5973 90.0007 19.9589 −3.0180 90.0007 21.5494 −0.9727 90.0007 20.1329 −3.3331 90.0007 21.7179 −1.3480 90.0007 20.3082 −3.6482 90.0007 21.8851 −1.7234 90.0007 20.4822 −3.9647 90.0007 22.0508 −2.1001 90.0007 20.6562 −4.2797 90.0007 22.2152 −2.4769 90.0007 20.8288 −4.5962 90.0007 22.3796 −2.8550 90.0007 21.0028 −4.9113 90.0007 22.5426 −3.2331 90.0007 21.1768 −5.2278 90.0007 22.7043 −3.6112 90.0007 21.3494 −5.5428 90.0007 22.8646 −3.9893 90.0007 21.5220 −5.8593 90.0007 23.0235 −4.3688 90.0007 21.6946 −6.1758 90.0007 23.1824 −4.7483 90.0007 21.8659 −6.4922 90.0007 23.3400 −5.1277 90.0007 22.0371 −6.8087 90.0007 23.4975 −5.5086 90.0007 22.2084 −7.1251 90.0007 23.6537 −5.8881 90.0007 22.3796 −7.4430 90.0007 23.8098 −6.2703 90.0007 22.5495 −7.7608 90.0007 23.9660 −6.6511 90.0007 22.7194 −8.0773 90.0007 24.1208 −7.0334 90.0007 22.8892 −8.3965 90.0007 24.2756 −7.4156 90.0007 23.0577 −8.7143 90.0007 24.4304 −7.7978 90.0007 23.2262 −9.0335 90.0007 24.5839 −8.1800 90.0007 23.3934 −9.3527 90.0007 24.7359 −8.5622 90.0007 23.5605 −9.6719 90.0007 24.8866 −8.9444 90.0007 23.7263 −9.9925 90.0007 25.0360 −9.3267 90.0007 23.8907 −10.3130 90.0007 25.1853 −9.7103 90.0007 24.0537 −10.6336 90.0007 25.3319 −10.0925 90.0007 24.2154 −10.9555 90.0007 25.4798 −10.4761 90.0007 24.3743 −11.2789 90.0007 25.6278 −10.8596 90.0007 24.5318 −11.6022 90.0007 25.7785 −11.2460 90.0007 24.6880 −11.9255 90.0007 25.9292 −11.6337 90.0007 24.8496 −12.2502 90.0007 26.0415 −12.0269 90.0007 25.0346 −12.5584 90.0007 26.0032 −12.4255 90.0007 25.3483 −12.7365 90.0007 25.7059 −12.7036 90.0007 25.7059 −12.7036 90.0007 5.1469 14.5558 100.0000 5.1469 14.5558 100.0000 5.1469 14.8202 100.0000 5.2127 14.3352 100.0000 5.2168 15.0750 100.0000 5.3346 14.1380 100.0000 5.2784 15.1915 100.0000 5.4141 14.0544 100.0000 5.3401 15.3079 100.0000 5.4935 13.9708 100.0000 5.6018 15.6202 100.0000 5.7853 13.7653 100.0000 5.9141 15.8874 100.0000 6.1114 13.6256 100.0000 6.2443 16.1258 100.0000 6.4580 13.5461 100.0000 6.5936 16.3340 100.0000 6.8142 13.5105 100.0000 6.9662 16.5039 100.0000 7.1731 13.4996 100.0000 7.3512 16.6326 100.0000 7.5348 13.4968 100.0000 7.7471 16.7148 100.0000 7.8937 13.4886 100.0000 8.1512 16.7518 100.0000 8.2526 13.4626 100.0000 8.5581 16.7464 100.0000 8.6061 13.4132 100.0000 8.9623 16.7039 100.0000 8.9568 13.3324 100.0000 9.3609 16.6244 100.0000 9.3034 13.2187 100.0000 9.7514 16.5107 100.0000 9.6418 13.0735 100.0000 10.1322 16.3655 100.0000 9.9664 12.9023 100.0000 10.4993 16.1929 100.0000 10.2760 12.7091 100.0000 10.8528 15.9970 100.0000 10.5692 12.4954 100.0000 11.1939 15.7792 100.0000 10.8514 12.2625 100.0000 11.5254 15.5435 100.0000 11.1213 12.0159 100.0000 11.8446 15.2915 100.0000 11.3802 11.7556 100.0000 12.1543 15.0284 100.0000 11.6282 11.4843 100.0000 12.4529 14.7517 100.0000 11.8652 11.2062 100.0000 12.7406 14.4654 100.0000 12.0926 10.9227 100.0000 13.0201 14.1695 100.0000 12.3132 10.6350 100.0000 13.2900 13.8653 100.0000 12.5269 10.3432 100.0000 13.5502 13.5544 100.0000 12.7365 10.0473 100.0000 13.8023 13.2365 100.0000 12.9406 9.7486 100.0000 14.0475 12.9146 100.0000 13.1406 9.4472 100.0000 14.2845 12.5885 100.0000 13.3365 9.1431 100.0000 14.5147 12.2584 100.0000 13.5283 8.8376 100.0000 14.7407 11.9241 100.0000 13.7174 8.5280 100.0000 14.9613 11.5857 100.0000 13.9037 8.2184 100.0000 15.1764 11.2446 100.0000 14.0873 7.9060 100.0000 15.3874 10.9007 100.0000 14.2681 7.5923 100.0000 15.5956 10.5541 100.0000 14.4462 7.2758 100.0000 15.7983 10.2062 100.0000 14.6229 6.9594 100.0000 15.9984 9.8541 100.0000 14.7983 6.6416 100.0000 16.1956 9.5020 100.0000 14.9723 6.3237 100.0000 16.3902 9.1472 100.0000 15.1449 6.0045 100.0000 16.5820 8.7910 100.0000 15.3161 5.6840 100.0000 16.7724 8.4335 100.0000 15.4860 5.3634 100.0000 16.9601 8.0745 100.0000 15.6545 5.0414 100.0000 17.1450 7.7156 100.0000 15.8230 4.7209 100.0000 17.3286 7.3553 100.0000 15.9901 4.3976 100.0000 17.5108 6.9936 100.0000 16.1573 4.0756 100.0000 17.6916 6.6320 100.0000 16.3230 3.7523 100.0000 17.8725 6.2703 100.0000 16.4888 3.4290 100.0000 18.0506 5.9073 100.0000 16.6546 3.1057 100.0000 18.2273 5.5428 100.0000 16.8190 2.7824 100.0000 18.4026 5.1784 100.0000 16.9834 2.4591 100.0000 18.5766 4.8140 100.0000 17.1477 2.1344 100.0000 18.7492 4.4496 100.0000 17.3108 1.8097 100.0000 18.9218 4.0838 100.0000 17.4752 1.4864 100.0000 19.0917 3.7181 100.0000 17.6382 1.1617 100.0000 19.2602 3.3509 100.0000 17.8012 0.8370 100.0000 19.4287 2.9838 100.0000 17.9642 0.5124 100.0000 19.5959 2.6152 100.0000 18.1273 0.1877 100.0000 19.7616 2.2481 100.0000 18.2903 −0.1370 100.0000 19.9260 1.8782 100.0000 18.4519 −0.4617 100.0000 20.0890 1.5097 100.0000 18.6150 −0.7864 100.0000 20.2521 1.1398 100.0000 18.7780 −1.1110 100.0000 20.4137 0.7699 100.0000 18.9410 −1.4357 100.0000 20.5754 0.3987 100.0000 19.1027 −1.7604 100.0000 20.7357 0.0274 100.0000 19.2657 −2.0851 100.0000 20.8946 −0.3439 100.0000 19.4287 −2.4098 100.0000 21.0535 −0.7165 100.0000 19.5918 −2.7344 100.0000 21.2110 −1.0891 100.0000 19.7548 −3.0591 100.0000 21.3672 −1.4617 100.0000 19.9178 −3.3838 100.0000 21.5234 −1.8344 100.0000 20.0808 −3.7071 100.0000 21.6782 −2.2070 100.0000 20.2439 −4.0318 100.0000 21.8316 −2.5810 100.0000 20.4069 −4.3565 100.0000 21.9851 −2.9550 100.0000 20.5713 −4.6798 100.0000 22.1371 −3.3290 100.0000 20.7343 −5.0045 100.0000 22.2878 −3.7044 100.0000 20.8973 −5.3291 100.0000 22.4385 −4.0784 100.0000 21.0603 −5.6538 100.0000 22.5892 −4.4537 100.0000 21.2247 −5.9771 100.0000 22.7385 −4.8291 100.0000 21.3878 −6.3018 100.0000 22.8879 −5.2058 100.0000 21.5508 −6.6265 100.0000 23.0358 −5.5812 100.0000 21.7138 −6.9512 100.0000 23.1838 −5.9579 100.0000 21.8782 −7.2758 100.0000 23.3317 −6.3361 100.0000 22.0399 −7.6005 100.0000 23.4783 −6.7128 100.0000 22.2029 −7.9252 100.0000 23.6249 −7.0909 100.0000 22.3645 −8.2499 100.0000 23.7715 −7.4690 100.0000 22.5276 −8.5759 100.0000 23.9153 −7.8471 100.0000 22.6879 −8.9006 100.0000 24.0592 −8.2252 100.0000 22.8495 −9.2267 100.0000 24.2017 −8.6033 100.0000 23.0084 −9.5527 100.0000 24.3428 −8.9814 100.0000 23.1673 −9.8788 100.0000 24.4811 −9.3595 100.0000 23.3263 −10.2062 100.0000 24.6209 −9.7377 100.0000 23.4824 −10.5322 100.0000 24.7592 −10.1158 100.0000 23.6386 −10.8596 100.0000 24.9003 −10.4952 100.0000 23.7948 −11.1884 100.0000 25.0456 −10.8761 100.0000 23.9496 −11.5172 100.0000 25.1894 −11.2583 100.0000 24.1058 −11.8474 100.0000 25.2935 −11.6460 100.0000 24.2866 −12.1570 100.0000 25.2469 −12.0364 100.0000 24.5976 −12.3337 100.0000 24.9497 −12.3050 100.0000 24.9497 −12.3050 100.0000

It will also be appreciated that the airfoil 52 disclosed in the above Table I may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Table I may be scaled upwardly or downwardly such that the airfoil profile shape remains unchanged. A scaled version of the coordinates in Table I would be represented by X, Y, and Z coordinate values of Table I, with the X, Y, and Z non-dimensional coordinate values converted to inches, multiplied or divided by a constant number.

An important term in this disclosure is “profile”. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in Table I. The actual profile on a manufactured turbine rotor blade will be different than those in Table I and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, a +or −5% profile tolerance is used herein. The X, Y, and Z values are all non-dimensionalized relative to the airfoil height.

The disclosed airfoil shape optimizes and is specific to machine conditions and specifications. It provides a unique profile to achieve: 1) interaction between other stages in the turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical rotor blade or airfoil loadings. The disclosed locus of points defined in Table I allows the gas turbine 12 or any other suitable turbine to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil 52 may be adopted as long as 1) interaction between other stages in the pressure turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical blade loadings are maintained in the scaled turbine. The airfoil 52 described herein thus improves overall gas turbine 12 efficiency. Specifically, the airfoil 52 provides a desired turbine efficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 52 also meets all aeromechanics and stress requirements. The turbine rotor blade 50 described herein has very specific aerodynamic design requirements. Significant cross-functional design effort was required to meet these design goals. The airfoil 52 of the rotor blade 50, thus, is of a specific shape to meet aerodynamic, mechanical, and heat transfer requirements in an efficient and cost-effective manner.

Further, it should be understood that exemplary embodiments of the present disclosure may include the entirety of the nominal airfoil profile set forth in Table I or portions thereof. Such portions may include a portion of the pressure side (or “pressure side portion”), a portion of the suction side (or “suction side portion”), and portions of both the pressure side and suction side.

Thus, exemplary embodiments of the present disclosure include a turbine rotor blade having an airfoil that includes a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a height of the airfoil defined along the Z axis. The X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value. The pressure side sections may be joined smoothly with one another to form the pressure side portion.

Exemplary embodiments of the present disclosure also include a turbine rotor blade having an airfoil that includes a suction side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a suction side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a height of the airfoil defined along the Z axis. The X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value. The suction side sections may be joined smoothly with one another to form the suction side portion.

Exemplary embodiment of the present disclosure also include a turbine engine that has an airfoil, wherein the airfoil includes: a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I; and a suction side portion of the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in Table I. The Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a height of the airfoil defined along the Z axis. The X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value. The pressure side sections may be joined smoothly with one another to form the pressure side portion. The X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value. The suction side sections may be joined smoothly with one another to form the suction side portion.

A height of each of the suction side portion and pressure side portion may be defined along the Z axis. The height of each of the suction side portion and pressure side portion may be less than or equal to the height of the airfoil. According to exemplary embodiments, the height of the suction side portion and the height of the pressure side portion may be substantially the same. According to exemplary embodiments, the suction side portion and the pressure side portion may each start at a common distance relative to a base of the airfoil and extend toward a tip of the airfoil. According to exemplary embodiments, the height of the suction side portion and/or the height of the pressure side portion may each be equal to or greater than 50% of the height of the airfoil. According to other embodiments, the height of the suction side portion and/or the height of the pressure side portion may each be equal to or greater than 75% of the height of the airfoil. According to other embodiments, the height of the suction side portion and the height of the pressure side portion may each be equal to 100% of the height of the airfoil.

As already described, the turbine engine may include a combustion or gas turbine that has a compressor, combustor, and turbine. The airfoil of the present disclosure may be configured as the airfoil of a turbine rotor blade, i.e., a rotor blade within the turbine of the gas turbine. More specifically, the airfoil of the present disclosure may be the airfoil of a turbine rotor blade that is configured to function as a second stage rotor blade in the turbine. In such cases, the turbine includes a second stage that has a row of circumferentially spaced nozzles and a row of circumferentially spaced rotor blades, with the airfoil of the present disclosure being configured as the airfoil of each of the rotor blades within the second stage row of rotor blades.

Along with the airfoil, the shape or contour of the platform impacts aerodynamic characteristics and losses of the rotor blade and must satisfy system requirements of aerodynamic and mechanical blade loading and efficiency. The aerodynamic characteristics and losses associated with the platform, separately, as well as the manner in which the platform functions in tandem with the airfoil and/or fillets, may significantly affect performance, thrust, efficiency, and power. Embodiments of the present disclosure include one or more platform contours, which may be coupled with the airfoil shape disclosed above or used separately. As provided below, to define the contour of the platform there is a unique set or locus of points in space that meets the stage requirements and that can be manufactured. This unique locus of points satisfies the requirements for stage efficiency and, as will be appreciated, are arrived at by iteration between aerodynamic and mechanical loadings and enable the turbine to run in an efficient, safe and smooth manner. These points are unique and specific to the system.

Turning now to FIG. 3, a top view is provided of an endwall or platform 66, which is the surface from which the airfoil 52 of the rotor blade 50 extends. In accordance with an alternative embodiment of the present disclosure, a locus of points—each of which are represented as points on the illustrated contour lines of FIG. 3—defines a specific contour of a platform of a turbine rotor blade. These points are set forth in a set of points with X′, Y′, and Z′ dimensions relative to a reference origin coordinate system, as provided in Table II and shown in FIG. 3, respectively. Embodiments of the present disclosure, thus, include a rotor blade having a non-axisymmetric platform contour that enhances performance, efficiency and/or durability of the rotor blade when compared with conventional designs.

More specifically, the Cartesian coordinate system of X′, Y′, and Z′ values given in Table II below defines a surface shape or contour of the platform 66 of the turbine rotor blade 50 at various locations or points defined along contour lines 87. The contour lines 87 extend along the surface or surface area (also “total surface area”) of the platform 66, which is defined between an outer periphery or edges of the platform 66—which, as indicated, may be referred to as a leading edge 88, trailing edge 90, pressure edge 94, and suction edge 96—and a base of the airfoil 52 (i.e., the location at which the platform 66 terminates into the airfoil 52 and/or the fillet 72 of airfoil 52). As shown in FIG. 3, the point data origin 96 is defined at a position within the footprint of the airfoil 52, for example, a point near a central portion of the footprint of the airfoil 52. The point data origin 96 corresponds to the non-dimensional Z′ value of Table II (presented below) at Z′ equals 0.

The coordinate values for the X′, Y′, and Z′ coordinates are set forth in non-dimensionalized units in Table II, although units of dimensions may be used when the values are appropriately converted. That is, the X′, Y′, and Z′ values set forth in Table II are expressed in non-dimensional form (X′, Y′, and Z′) from 0% to 100%, which may be converted by multiplying each by the radial span 70 (as shown in FIG. 2) or height of the airfoil. As one example, the Cartesian coordinate values of X′, Y′, and Z′ may be convertible to dimensional distances by multiplying the X′, Y′, and Z′ values by a height of the airfoil at the leading edge 58 and/or multiplying by a constant number. As another example, the Cartesian coordinate values of X′, Y′, and Z′ may be convertible to dimensional distances by multiplying the X′, Y′, and Z′ values by a height of the airfoil at the trailing edge 60 and/or multiplying by a constant number. Thus, to convert the Z′ value to a Z′ coordinate value of the platform contour, for example, in inches, the non-dimensional Z′ value given in Table II is multiplied by the height of the airfoil in inches.

As described above, the Cartesian coordinate system has orthogonally-related X′, Y′, and Z′ axes, where the X′ axis lies generally parallel to a centerline of the rotor shaft 14, i.e., the rotary axis and a positive X′ coordinate value is axial toward an aft, i.e., exhaust end, of the turbine 10. The positive Y′ coordinate value extends tangentially in the direction of rotation of the rotor, and the positive Z′ coordinate value extends radially outwardly toward the radial tip 68 of the airfoil 52. All the values in Table II are given at room temperature.

By defining X′ and Y′ coordinate values at selected locations in a Z′ direction normal to the X′, Y′ plane, the contour of the platform is shown via several contour lines, each of which having multiple points spaced at regular intervals. By connecting the X′ and Y′ values of each of the contour lines with smooth continuing arcs, each contour line at each distance Z′ can be determined. The overall contour of the platform of the various surface locations can then be determined by smoothly connecting the adjacent contour lines to one another to form the platform.

The Table II values are generated and shown to four decimal places for determining the contour of the platform. As the turbine rotor blade heats up during operation of the gas turbine, mechanical stresses and elevated temperatures will cause a change in the X′, Y′, and Z′ values. Accordingly, it should be understood that the values for the nominal platform contour given in Table II represent ambient, non-operating or non-hot conditions (e.g., room temperature) and are for an uncoated platform. Further, there are typical manufacturing tolerances as well as coatings which may be accounted for in the actual shape or contour of the platform 66. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/−values, including any coating thicknesses, may be additive to the X′, Y′ and/or Z′ values given in Table II below. Accordingly, a distance of +/−5% in a direction normal to any platform surface location or about +/−5% of the length of the chord 62 in a direction nominal to any platform surface location may define a platform contour envelope for this particular platform design, i.e., a range of variation between measured points on the actual platform surface at nominal cold or room temperature and the ideal position of those points as given in Table II below at the same temperature. According to another example, a tolerance of about 10-20% of a thickness of the airfoil's trailing edge 60 in a direction normal to any platform surface location may define a range of variation between measured points on an actual platform surface and ideal positions as embodied by the invention in Table II. As should further be understood, the data provided in Table II is scalable and the geometry pertains to all aerodynamic scales and/or RPM ranges. The design of the platform 66 for the turbine rotor blade 50 is robust to this range of variation without impairment of mechanical and aerodynamic functions.

TABLE II X′ (%) Y′ (%) Z′ (%) 7.10323 −4.29481 −3.30160 7.90465 −4.22084 −3.30160 6.39633 −3.90438 −3.30160 8.65676 −3.90301 −3.30160 9.41434 −3.60299 −3.30160 10.18289 −3.33037 −3.30160 10.96239 −3.08788 −3.30160 11.75149 −2.88376 −3.30160 12.55017 −2.71799 −3.30160 13.35708 −2.59470 −3.30160 14.16809 −2.50976 −3.30160 14.98185 −2.46044 −3.30160 13.17077 −12.99815 −3.93178 12.48853 −12.57209 −3.93178 11.77067 −12.20906 −3.93178 11.01582 −11.92958 −3.93178 8.63210 −11.81314 −3.93178 10.23084 −11.75560 −3.93178 9.42941 −11.71039 −3.93178 7.53887 −6.85663 −3.93178 6.70457 −6.57168 −3.93178 8.35811 −6.48538 −3.93178 9.14446 −6.03329 −3.93178 5.99630 −6.00452 −3.93178 9.94452 −5.60312 −3.93178 5.27707 −5.45243 −3.93178 10.76238 −5.20995 −3.93178 11.60079 −4.86335 −3.93178 4.61264 −4.83595 −3.93178 12.45976 −4.57292 −3.93178 13.33790 −4.34413 −3.93178 14.23111 −4.18385 −3.93178 17.85328 −4.13179 −3.93178 15.13391 −4.08932 −3.93178 16.94774 −4.07562 −3.93178 16.04082 −4.05781 −3.93178 6.88266 12.43236 −3.93178 12.96527 12.62552 −3.93178 11.75286 13.18446 −3.93178 7.82245 13.35708 −3.93178 10.46373 13.52832 −3.93178 9.13076 13.60093 −3.93178 15.64765 −13.37078 −4.56196 14.78046 −12.35427 −4.56196 13.89410 −11.35420 −4.56196 6.00589 −11.00760 −4.56196 13.02281 −10.34043 −4.56196 5.95246 −9.78834 −4.56196 12.30221 −9.22118 −4.56196 5.51682 −8.64991 −4.56196 12.24604 −7.91972 −4.56196 4.75786 −7.69094 −4.56196 13.05432 −6.87581 −4.56196 3.88657 −6.82923 −4.56196 14.20645 −6.20864 −4.56196 20.80142 −6.06480 −4.56196 3.09473 −5.89629 −4.56196 19.47668 −5.88670 −4.56196 15.48736 −5.83465 −4.56196 18.14919 −5.74012 −4.56196 16.81485 −5.69902 −4.56196 2.55360 −4.80307 −4.56196 16.38057 11.37886 −4.56196 5.13734 11.63230 −4.56196 15.76409 12.04329 −4.56196 15.12843 12.68991 −4.56196 5.60038 12.83924 −4.56196 14.47222 13.31598 −4.56196 6.00452 14.06809 −4.56196 6.25522 15.33393 −4.56196 17.41900 −13.82971 −5.19214 16.83129 −12.85978 −5.19214 16.27372 −11.87479 −5.19214 15.79012 −10.85006 −5.19214 3.99479 −10.52264 −5.19214 15.50106 −9.75820 −5.19214 3.49476 −9.52531 −5.19214 15.69012 −8.65813 −5.19214 2.82211 −8.63210 −5.19214 23.17556 −8.08686 −5.19214 22.05494 −7.92383 −5.19214 16.49291 −7.87999 −5.19214 2.13850 −7.74711 −5.19214 20.94116 −7.71423 −5.19214 19.82191 −7.53750 −5.19214 17.56285 −7.52654 −5.19214 18.69306 −7.44983 −5.19214 1.58915 −6.77307 −5.19214 1.23981 −5.71272 −5.19214 1.09323 −4.60442 −5.19214 18.62319 10.09932 −5.19214 3.47284 10.68840 −5.19214 18.03000 10.94596 −5.19214 17.43270 11.78848 −5.19214 3.93452 12.42962 −5.19214 16.83540 12.62963 −5.19214 4.12905 14.21741 −5.19214 3.75916 15.96959 −5.19214 18.93280 −14.25303 −5.82232 18.46565 −13.19679 −5.82232 18.09713 −12.10220 −5.82232 17.96150 −10.95965 −5.82232 25.10994 −10.14179 −5.82232 23.96329 −10.01849 −5.82232 18.39441 −9.91712 −5.82232 1.29872 −9.83218 −5.82232 22.83581 −9.76505 −5.82232 21.70834 −9.51435 −5.82232 19.41503 −9.41297 −5.82232 20.56579 −9.35818 −5.82232 0.83019 −8.97733 −5.82232 0.43017 −8.08960 −5.82232 0.12193 −7.16487 −5.82232 −0.08220 −6.21275 −5.82232 −0.17398 −5.24282 −5.82232 −0.14659 −4.27016 −5.82232 20.64251 8.60607 −5.82232 1.77957 9.45544 −5.82232 20.14522 9.45681 −5.82232 19.65340 10.31030 −5.82232 2.02480 10.66100 −5.82232 19.17392 11.17200 −5.82232 2.16727 11.88301 −5.82232 18.71772 12.04466 −5.82232 2.13302 13.11186 −5.82232 1.87958 14.31468 −5.82232 1.47544 15.47640 −5.82232 1.07131 16.63950 −5.82232 20.41921 −14.68868 −6.45250 20.17672 −13.74889 −6.45250 20.10960 −12.78444 −6.45250 26.04288 −12.26522 −6.45250 27.00322 −12.17070 −6.45250 25.08939 −12.09672 −6.45250 20.45483 −11.89534 −6.45250 24.15371 −11.84054 −6.45250 23.21529 −11.59120 −6.45250 21.29461 −11.44736 −6.45250 22.26043 −11.42270 −6.45250 −0.73978 −9.21433 −6.45250 −1.13158 −7.87999 −6.45250 −1.39188 −6.51277 −6.45250 −1.48503 −5.12501 −6.45250 −1.37544 −3.73861 −6.45250 22.60977 6.78540 −6.45250 −0.10001 7.66354 −6.45250 22.06179 7.91013 −6.45250 0.13015 8.82800 −6.45250 21.53709 9.04583 −6.45250 0.28358 10.00479 −6.45250 21.05350 10.20070 −6.45250 0.32057 11.18981 −6.45250 20.67813 11.39256 −6.45250 0.23015 12.37345 −6.45250 0.03699 13.54339 −6.45250 −0.20823 14.70512 −6.45250 −0.44798 15.86684 −6.45250 −0.62881 17.03952 −6.45250 22.07685 −15.20515 −7.08268 27.82245 −14.52154 −7.08268 26.84567 −14.48455 −7.08268 22.25906 −14.24892 −7.08268 25.89903 −14.22015 −7.08268 28.69101 −14.08453 −7.08268 24.96061 −13.92013 −7.08268 24.00575 −13.68724 −7.08268 23.02760 −13.68450 −7.08268 −2.46866 −8.68827 −7.08268 −2.66320 −7.70601 −7.08268 −2.79745 −6.71416 −7.08268 −2.86595 −5.71546 −7.08268 −2.86458 −4.71539 −7.08268 −2.78101 −3.71806 −7.08268 −2.62484 −2.72895 −7.08268 −2.33304 4.36057 −7.08268 24.53045 4.70580 −7.08268 24.12083 5.70313 −7.08268 −2.07137 5.97438 −7.08268 23.73587 6.71142 −7.08268 −1.78779 7.58408 −7.08268 23.39475 7.73478 −7.08268 23.15775 8.78690 −7.08268 −1.58641 9.20611 −7.08268 22.89883 9.83218 −7.08268 −1.53161 10.83910 −7.08268 22.62210 10.87472 −7.08268 −1.62888 12.47072 −7.08268 −1.82204 14.09412 −7.08268 −2.01932 15.71614 −7.08268 −2.12480 17.34776 −7.08268 28.73484 −17.00801 −7.71286 27.69779 −16.84362 −7.71286 29.68833 −16.60525 −7.71286 26.70320 −16.49154 −7.71286 25.69628 −16.17782 −7.71286 24.65374 −16.15727 −7.71286 30.33221 −15.77368 −7.71286 −4.44688 −7.55942 −7.71286 −4.59758 −5.77848 −7.71286 −4.63319 −3.99068 −7.71286 −4.57292 −2.20426 −7.71286 −4.55237 −0.41784 −7.71286 −4.56470 1.36996 −7.71286 26.54154 2.17138 −7.71286 −4.53730 3.15775 −7.71286 26.18947 3.20570 −7.71286 25.88396 4.25372 −7.71286 −4.36879 4.93595 −7.71286 25.68121 5.32502 −7.71286 29.89246 5.37434 −7.71286 28.83622 5.60723 −7.71286 30.68292 6.01822 −7.71286 27.85670 6.08946 −7.71286 25.84972 6.37989 −7.71286 26.85937 6.53058 −7.71286 −4.12083 6.70731 −7.71286 30.57333 7.08953 −7.71286 30.07877 8.06083 −7.71286 −3.88931 8.47866 −7.71286 29.43215 8.94034 −7.71286 −3.76327 10.26235 −7.71286 −3.73724 12.04877 −7.71286 −3.76190 13.83656 −7.71286 −3.77423 15.62436 −7.71286 −3.71258 17.41078 −7.71286 31.60627 −18.15467 −8.34304 31.86520 −17.54778 −8.34304 32.11864 −16.93952 −8.34304 32.39948 −16.34359 −8.34304 32.70224 −15.75724 −8.34304 29.34174 −2.46592 −8.34304 29.01158 −1.48366 −8.34304 28.72526 −0.48770 −8.34304 28.52387 0.52743 −8.34304 32.46935 0.60963 −8.34304 31.46380 0.61237 −8.34304 30.52538 1.04802 −8.34304 33.02418 1.45763 −8.34304 29.60477 1.52476 −8.34304 28.64306 1.53435 −8.34304 33.21734 2.47414 −8.34304 33.29954 3.50709 −8.34304 33.33516 4.54278 −8.34304 33.25570 5.57298 −8.34304 32.92280 6.55250 −8.34304 32.42962 7.46352 −8.34304 31.84328 8.31838 −8.34304 33.69546 −18.73005 −8.97322 33.81601 −18.25467 −8.97322 33.96397 −17.78615 −8.97322 34.18042 −17.34502 −8.97322 34.45167 −16.93678 −8.97322

It will also be appreciated that the platform contour disclosed in the above Table II may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Table II may be scaled upwardly or downwardly such that the relative surface shape of the platform remains unchanged. A scaled version of the coordinates in Table II would be represented by X′, Y′, and Z′ coordinate values of Table II, with the X′, Y′, and Z′ non-dimensional coordinate values converted to inches, multiplied or divided by a constant number.

An important term in this disclosure is “profile”. The profile is the range of the variation between measured points on an actual platform surface and the ideal position listed in Table II. The actual profile on a manufactured turbine rotor blade will be different than those in Table II and the design is robust to the variation or tolerances described above, meaning that mechanical and aerodynamic function are not impaired.

The disclosed platform contour optimizes and is specific to machine conditions and specifications. In use, it provides a unique surface contour that achieves: 1) aerodynamic efficiency; and 2) normalized aerodynamic and mechanical rotor blade or platform loading. The disclosed locus of points defined in Table II allows the gas turbine 12 or any other suitable turbine to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed platform contour may be adopted as long as 1) aerodynamic efficiency; and 2) normalized aerodynamic and mechanical rotor blade loadings are maintained in the scaled turbine. The platform 66 described herein thus improves overall gas turbine 12 efficiency. The disclosed platform 66 also meets all aeromechanics and stress requirements. The turbine rotor blade 50 described herein has very specific aerodynamic design requirements. Significant cross-functional design effort was required to meet these design goals. The platform 66 of the rotor blade 50, thus, is of a specific shape to meet aerodynamic, mechanical, and heat transfer requirements in an efficient and cost-effective manner, and, in accordance with alternative embodiments, may be use to advantage in conjunction with the airfoil disclosed above.

Further, it should be understood that exemplary embodiments of the present disclosure may include the entirety of the nominal surface shape or contour set forth in Table II or portions thereof. Such portions may include a portion of the platform 66 adjacent to or near the pressure edge 94, a portion of the platform 66 adjacent to or near the suction edge 96, a portion of the platform 66 adjacent to or near the leading edge 88, and/or a portion of the platform 66 adjacent or near the trailing edge 90. Such portions further may include a portion of the platform 66 defined between the pressure edge 94 and the airfoil 52, a portion of the platform 66 defined between the suction edge 96 and the airfoil.

Thus, embodiments of the present disclosure may include a turbine rotor blade including an airfoil that extends from a platform. The platform may include a first portion of a nominal platform contour substantially in accordance with Cartesian coordinate values of X′, Y′, and Z′ as set forth in Table II. The Cartesian coordinate values of X′, Y′, and Z′ are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X′, Y′, and Z′ by a height of the airfoil defined along a Z′ axis. The X′ and Y′ values of the first portion are coordinate values that, when connected by smooth continuing arcs, define contour lines of the first portion of the nominal airfoil profile at each Z′ coordinate value. The contour lines may be joined smoothly with one another to form the first portion. As defined above, a total surface area of the platform is defined between an outer periphery of the platform, which is defined by a leading edge, trailing edge, pressure edge, and suction edge of the platform, and a base of the airfoil. In accordance with exemplary embodiments, the surface area of the first portion may be equal to or greater than 50% of the total surface area of the platform. In accordance with other embodiments, the surface area of the first portion may be equal to or greater than 75% of the total surface area of the platform. In accordance with still other embodiments, the surface area of the first portion may be equal to 100% of the total surface area of the platform.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims. 

What is claimed:
 1. A turbine rotor blade including an airfoil extending from a platform, wherein the platform comprises a first portion of a nominal platform contour substantially in accordance with Cartesian coordinate values of X′, Y′, and Z′ as set forth in Table II, wherein: the Cartesian coordinate values of X′, Y′, and Z′ are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X′, Y′, and Z′ by a height of the airfoil defined along a Z′ axis; the X′ and Y′ values of the first portion are coordinate values that, when connected by smooth continuing arcs, define contour lines of the first portion of the nominal airfoil profile at each Z′ coordinate value; and the contour lines are joined smoothly with one another to form the first portion.
 2. The turbine rotor blade of claim 1, wherein the nominal platform contour lies in an envelope within +/−5% of a chord length of the airfoil in a direction normal to any of the contour lines.
 3. The turbine rotor blade of claim 1, wherein a total surface area of the platform is defined between an outer periphery of the platform, which is defined by a leading edge, trailing edge, pressure edge, and suction edge of the platform, and a base of the airfoil.
 4. The turbine rotor blade of claim 3, wherein a surface area of the first portion is equal to or greater than 50% of the total surface area of the platform; and wherein the height of the airfoil is between 3 and 10 inches.
 5. The turbine rotor blade of claim 3, wherein a surface area of the first portion is equal to or greater than 75% of the total surface area of the platform; and wherein the turbine rotor blade is configured to function as a second stage turbine rotor blade in a turbine.
 6. The turbine rotor blade of claim 3, wherein a surface area of the first portion is equal to 100% of the total surface area of the platform.
 7. A turbine engine that includes a rotor blade having an airfoil that comprises: a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I; a suction side portion of the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in Table I; wherein: the Cartesian coordinate values of X, Y, and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a height of the airfoil defined along a Z axis; the X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value, the pressure side sections being joined smoothly with one another to form the pressure side portion; and the X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value, the suction side sections being joined smoothly with one another to form the suction side portion.
 8. The turbine engine of claim 7, wherein the turbine engine comprises a gas turbine having a compressor, a combustor, and a turbine; and wherein the airfoil comprises a rotor blade in the turbine.
 9. The turbine engine of claim 8, wherein the rotor blade is a second stage rotor blade in the turbine.
 10. The turbine engine of claim 8, wherein the nominal airfoil profile lies in an envelope within +/−20% of a thickness of a trailing edge of the airfoil in a direction normal to any of the suction side and pressure side sections; and wherein: a height of the suction side portion is defined along the Z axis, and wherein the height of the suction side portion is less than or equal to the height of the airfoil; and a height of the pressure side portion is defined along the Z axis, and wherein the height of the pressure side portion is less than or equal to the height of the airfoil.
 11. The turbine engine of claim 10, wherein the height of the suction side portion and the height of the pressure side portion are substantially the same; wherein the height of the suction side portion and the height of the pressure side portion are each equal to or greater than 50% of the height of the airfoil; and wherein the suction side portion and the pressure side portion start at a common distance relative to a base of the airfoil and extend toward a tip of the airfoil.
 12. The turbine engine of claim 11, wherein the height of the suction side portion and the height of the pressure side portion are each equal to or greater than 75% of the height of the airfoil.
 13. The turbine engine of claim 11, wherein the height of the suction side portion and the height of the pressure side portion are each equal to 100% of the height of the airfoil.
 14. The turbine engine of claim 11, wherein the turbine comprises a second stage that includes a row of second stage nozzles adjacent to a row of second stage rotor blades; and wherein a plurality of second stage rotor blades contained within the row of second stage rotor blades comprises the airfoil.
 15. A turbine rotor blade comprising an airfoil that extends from a platform; wherein the airfoil comprises at least one of: a) a pressure side portion of a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of a pressure side as set forth in Table I; and b) a suction side portion of the nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of the suction side as set forth in Table I; wherein: the Cartesian coordinate values of X, Y, and Z of Table I are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a height of the airfoil defined along a Z axis; the X and Y values of the pressure side are coordinate values that, when connected by smooth continuing arcs, define pressure side sections of the pressure side portion of the nominal airfoil profile at each Z coordinate value, the pressure side sections being joined smoothly with one another to form the pressure side portion; and the X and Y values of the suction side are coordinate values that, when connected by smooth continuing arcs, define suction side sections of the suction side portion of the nominal airfoil profile at each Z coordinate value, the suction side sections being joined smoothly with one another to form the suction side portion; wherein the platform comprises a first portion of a nominal platform contour substantially in accordance with Cartesian coordinate values of X′, Y′, and Z′ as set forth in Table II; wherein: the Cartesian coordinate values of X′, Y′, and Z′ of Table II are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X′, Y′, and Z′ by the height of the airfoil defined along a Z′ axis; the X′ and Y′ values of the first portion are coordinate values that, when connected by smooth continuing arcs, define contour lines of the first portion of the nominal airfoil profile at each Z′ coordinate value; and the contour lines are joined smoothly with one another to form the first portion.
 16. The turbine rotor blade of claim 15, wherein the turbine rotor blade is configured to function as a second stage turbine rotor blade in a turbine; and wherein the height of the airfoil is between 3 and 10 inches.
 17. The turbine rotor blade of claim 15, wherein the airfoil comprises both of the pressure side portion and the suction side portion of the nominal airfoil profile; wherein: a height of the suction side portion is defined along the Z axis, and wherein the height of the suction side portion is less than or equal to the height of the airfoil; and a height of the pressure side portion is defined along the Z axis, and wherein the height of the pressure side portion is less than or equal to the height of the airfoil; wherein a total surface area of the platform is defined between an outer periphery of the platform, which is defined by a leading edge, trailing edge, pressure edge, and suction edge of the platform, and a base of the airfoil.
 18. The turbine rotor blade of claim 17, wherein the height of the suction side portion and the height of the pressure side portion are each equal to or greater than 50% of the height of the airfoil; and wherein a surface area of the first portion is equal to or greater than 50% of the total surface area of the platform.
 19. The turbine rotor blade of claim 17, wherein the height of the suction side portion and the height of the pressure side portion are each equal to or greater than 75% of the height of the airfoil; and wherein a surface area of the first portion is equal to or greater than 75% of the total surface area of the platform.
 20. The turbine rotor blade of claim 17, wherein the height of the suction side portion and the height of the pressure side portion are each equal to 100% of the height of the airfoil; and wherein a surface area of the first portion is equal to 100% of the total surface area of the platform. 